Subtle Price Discrimination and Surplus Extraction Under Uncertainty
15 Pages Posted: 26 May 2009 Last revised: 24 May 2013
Date Written: March 31, 2013
In this paper I provide a solution to Proebsting’s Paradox, an argument that appears to show that the investment rule known as the Kelly criterion can lead a decision maker to invest a higher fraction of his wealth the more unfavorable the odds he faces are and, as a consequence, risk an arbitrarily high proportion of his wealth on the outcome of a single event. I show that a large class of investment criteria, including ’fractional Kelly,’ also suffer from the same shortcoming and adapt ideas from the literature on price discrimination and surplus extraction to explain why this is so. I also derive a new criterion, dubbed the doubly conservative criterion, that is immune to the problem identified above. Immunity stems from the investor’s attitudes towards capital preservation and from him becoming rapidly pessimistic about his chances of winning the better odds he is offered.
Keywords: Kelly criterion, risk management, asset allocation, betting rules, price discrimination, expected utility theory
JEL Classification: D11, D81
Suggested Citation: Suggested Citation